Coefficient bounds for certain families of bi-univalent functions defined by Wanas operator

2021 ◽  
pp. 2250100
Author(s):  
Abbas Karem Wanas ◽  
Aqeel Ketab Al-Khafaji
Keyword(s):  
Univalent Functions ◽  
Upper Bounds ◽  
Coefficient Bounds ◽  
Special Cases

The main purpose of this paper is to find upper bounds for the second and third Taylor–Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Wanas operator. Further, we point out certain special cases for our results.

scholarly journals Coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions

2021 ◽  
Vol 66 (4) ◽  
pp. 659-666
Author(s):  
Abbas Kareem Wanas ◽  
◽  
Agnes Orsolya Pall-Szabo ◽  
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Special Cases

In the present paper, we introduce and study two new subclasses of analytic and $m$-fold symmetric bi-univalent functions defined in the open unit disk $U$. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients $\left| a_{m+1}\right|$ and $\left| a_{2m+1}\right|$. Also, we indicate certain special cases for our results.

scholarly journals Coefficient Bounds and Fekete-Szegӧ Problem for a New Subclasses of Holomorphic Bi-Univalent Functions Defined by Horadam polynomials

2021 ◽  
Vol 26 (2) ◽  
pp. 52-65
Author(s):  
Najah Ali Jiben Al-Ziadi ◽  
Abbas Kareem Wanas
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Special Cases

In the present paper, by making use the Horadam polynomials, we introduce and investigate two new subclasses  and  of the function class  of holomorphic bi-univalent functions in the open unit disk Δ. For functions belonging to this subclasses, we obtain upper bounds for the second and third coefficients and discuss Fekete-Szegӧ problem. Furthermore, we point out several new special cases of our results.

scholarly journals Coefficient estimates for families of bi-univalent functions defined by Ruscheweyh derivative operator

2021 ◽  
Vol 25 (1) ◽  
pp. 71-80
Author(s):  
Serap Bulut ◽  
Wanas Kareem
Keyword(s):  
Univalent Functions ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Special Cases

The main purpose of this manuscript is to find upper bounds for the second and third Taylor-Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Ruscheweyh derivative operator. Further, we point out certain special cases for our results.

scholarly journals Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

2019 ◽  
Vol 16 (1(Suppl.)) ◽  
pp. 0248
Author(s):  
Juma Et al.
Keyword(s):  
Differential Operator ◽  
Explicit Formula ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomials ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Bazilevic Functions

In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.          In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.  

scholarly journals Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

2019 ◽  
Vol 16 (1) ◽  
pp. 0248
Author(s):  
Juma Et al.
Keyword(s):  
Differential Operator ◽  
Explicit Formula ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomials ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Bazilevic Functions

In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.          In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.  

scholarly journals Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions

2021 ◽  
Vol 39 (4) ◽  
pp. 153-164
Author(s):  
Ahmad Zireh ◽  
Saideh Hajiparvaneh
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Initial Coefficient

‎In this paper‎, ‎we introduce and investigate a subclass‎ of analytic and bi-univalent functions which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric in the open unit disk U‎. Furthermore‎, ‎we find upper bounds for the initial coefficients $|a_{m‎ + ‎1}|$ and $|a_{2m‎ + ‎1}|$ for functions in this subclass‎. ‎The results presented in this paper would generalize and improve some recent works‎.

scholarly journals Coefficient Estimates for Bi-Univalent Functions in Connection with Symmetric Conjugate Points Related to Horadam Polynomial

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1888
Author(s):  
S. Melike Aydoğan ◽  
Zeliha Karahüseyin
Keyword(s):  
Univalent Functions ◽  
Conjugate Points ◽  
Coefficient Estimates ◽  
Open Disc ◽  
Coefficient Bounds ◽  
Special Cases

In the current study, we construct a new subclass of bi-univalent functions with respect to symmetric conjugate points in the open disc E, described by Horadam polynomials. For this subclass, initial Maclaurin coefficient bounds are acquired. The Fekete–Szegö problem of this subclass is also acquired. Further, some special cases of our results are designated.

scholarly journals Certain new subclasses of \(m\)-fold symmetric bi-pseudo-starlike functions using \(Q\)-derivative operator

2021 ◽  
Vol 5 (1) ◽  
pp. 42-50
Author(s):  
Timilehin Gideon Shaba ◽  
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Holomorphic Functions ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Special Cases

In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.

scholarly journals Coefficient Bounds for a New Subclasses of Bi-Univalent Functions Associated with Horadam Polynomials

2021 ◽  
Vol 20 ◽  
pp. 105-114
Author(s):  
Najah Ali Jiben Al-Ziadi
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds

\In this work we present and investigate three new subclasses of  the function class  of bi-univalent functions in the open unit disk  defined by means of the Horadam polynomials. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients  and . Also, we debate Fekete-Szegӧ inequality for functions belongs to these subclasses.    

scholarly journals Coefficient Bounds and Fekete-Szeg¨o inequality for a Certain Families of Bi-Prestarlike Functions Defined by (M,N)-Lucas Polynomials

2021 ◽  
Vol 20 ◽  
pp. 121-134
Author(s):  
Najah Ali Jiben Al-Ziadi ◽  
Abbas Kareem Wanas
Keyword(s):  
Unit Disk ◽  
Upper Bounds ◽  
Current Work ◽  
Series Expansions ◽  
Maclaurin Series ◽  
Coefficient Bounds ◽  
Lucas Polynomials ◽  
Special Cases

In the current work, we use the (M,N)-Lucas Polynomials to introduce a new families of holomorphic and bi-Prestarlike functions defined in the unit disk O and establish upper bounds for the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we debate Fekete-Szeg¨o problem for thesefamilies. Further, we point out several certain special cases for our results.

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